講座主題：Prevention of infinite-time blowup in a Keller-Segel system with density-suppressed motility
專家姓名：江杰
工作單位：中國(guó)科學(xué)院精密測(cè)量科學(xué)與技術(shù)創(chuàng)新研究院
講座時(shí)間：2025年05月31日 14:30-15:50
講座地點(diǎn)：煙臺(tái)大學(xué)承先圖書館報(bào)告廳
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this talk, we consider an initial-Neumann boundary value problem for a Keller-Segel system with non-local Fokker-Planck type diffusion and source terms. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension N≥2. In this talk, we will report our recent result that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of at most, the classical solution is uniformly-in-time bounded when N≤3, thus preventing the infinite-time explosion detected in the source-free counter-part. By contrast, we recall that there are finite-time blowups in Keller-Segel system with Fick type diffusion even when slightly super-linear degradation gets involved. Thus, our result reveals an important difference between Fokker-Planck type diffusion and Fick type diffusion in Keller-Segel models. We will first outline the comparison method developed by the speaker to study the homogeneous problem and we review some previous results concerning global boundedness as well as infinite blowups. Then, we show that an improved comparison argument by introducing a new auxiliary variable, together with a construction of an entropy-like inequality will yield to the desired blowup-prevention result.
主講人介紹：
江杰，2004年畢業(yè)于山東大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院基地班，2009年于復(fù)旦大學(xué)數(shù)學(xué)科學(xué)學(xué)院獲得理學(xué)博士學(xué)位，師從鄭宋穆教授. 2009年到2011年在北京應(yīng)用物理與計(jì)算數(shù)學(xué)研究所郭柏靈院士指導(dǎo)下從事博士后工作. 主要研究趨化方程、相場(chǎng)-流體方程組等非線性發(fā)展方程整體解的適定性、有界性、漸近性、爆破解等相關(guān)問題. 目前在CPDE, CVPDE, JDE, SIMA, Nonlinearity等國(guó)際數(shù)學(xué)刊物正式發(fā)表SCI論文31篇(通訊作者27篇). 獲得2021年度中國(guó)科學(xué)院精密測(cè)量院突出科技成果獎(jiǎng)，2023年湖北省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)優(yōu)秀青年學(xué)者獎(jiǎng). 主持多項(xiàng)國(guó)家自然科學(xué)基金等課題。
